Banach Journal of Mathematical Analysis

Lower and upper local uniform K-monotonicity in symmetric spaces

Maciej Ciesielski

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Abstract

Using the local approach to the global structure of a symmetric space E, we establish a relationship between strict K-monotonicity, lower (resp., upper) local uniform K-monotonicity, order continuity, and the Kadec–Klee property for global convergence in measure. We also answer the question: Under which condition does upper local uniform K-monotonicity coincide with upper local uniform monotonicity? Finally, we present a correlation between K-order continuity and lower local uniform K-monotonicity in a symmetric space E under some additional assumptions on E.

Article information

Source
Banach J. Math. Anal., Volume 12, Number 2 (2018), 314-330.

Dates
Received: 14 March 2017
Accepted: 12 April 2017
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1513674116

Digital Object Identifier
doi:10.1215/17358787-2017-0047

Mathematical Reviews number (MathSciNet)
MR3779716

Zentralblatt MATH identifier
06873503

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 46B20: Geometry and structure of normed linear spaces 46B42: Banach lattices [See also 46A40, 46B40]

Keywords
symmetric space Lorentz space K-order continuity lower (upper) local uniform K-monotonicity Kadec–Klee property for global convergence in measure

Citation

Ciesielski, Maciej. Lower and upper local uniform $K$ -monotonicity in symmetric spaces. Banach J. Math. Anal. 12 (2018), no. 2, 314--330. doi:10.1215/17358787-2017-0047. https://projecteuclid.org/euclid.bjma/1513674116


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